Mathematische Annalen

, Volume 355, Issue 2, pp 783–799 | Cite as

A simple separable exact C*-algebra not anti-isomorphic to itself

  • N. Christopher Phillips
  • Maria Grazia Viola


We give an example of an exact, stably finite, simple, separable C*-algebra D which is not isomorphic to its opposite algebra. Moreover, D has the following additional properties. It is stably finite, approximately divisible, has real rank zero and stable rank one, has a unique tracial state, and the order on projections over D is determined by traces. It also absorbs the Jiang-Su algebra Z, and in fact absorbs the 3 UHF algebra. We can also explicitly compute the K-theory of D, namely \({K_0 (D) \cong {\mathbb{Z}} [ \tfrac{1}{3}]}\) with the standard order, and K 1 (D) =  0, as well as the Cuntz semigroup of D, namely \({W (D) \cong {\mathbb{Z}} [ \tfrac{1}{3} ]_{+} \sqcup (0, \infty).}\)

Mathematics Subject Classification (2000)

46L35 46L37 46L40 46L54 


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of OregonEugeneUSA
  2. 2.Department of Mathematics and Interdisciplinary StudiesLakehead University-OrilliaOrilliaCanada

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